MLE results from a simple RBC model (King and Rebelo)

Hello all,

I am attempting to estimate (using maximum liklihood, not Bayesian) three of the parameters of a basic RBC model (discount rate, constant of rel risk aversion, stderr of the technology shock). I am using 20 years worth of data (quarterly, n = 80). The data file contains the percent deviation of real GDP from its trend (log actual - log filtered, where I use the HP filter, lambda = 1,600). I have specified the mode in the estimation to be mode_compute = 7.

The problem is that I get plausible values for the estimated means of the two parameters, but the standard deviations for both come back as 0.00 and the t-statistics come back extraordinarily high (in the neighborhood of 3.5 million!). The estimated results for the third parameter, the technological innovation, come back fine (s.d. ~= 0.02, t-stat. ~= 40).

The same issue occurs when I estimate the two parameters (discount rate, constant of rel risk aversion) in isolation of each other…zero s.d. and enormous t-stat.

How am I to interpret these results? Should I be using a different estimation routine?

Any help/ideas/insight regardless of triviality is appreciated!

P.S. I have uploaded the .mod file if that happens to help; it runs fine, so I am hoping someone can simply diagnose my issue from their past experience with the weird results I have written about above.
rep1.mod (1.38 KB)

Please provide the data file as well. You may need to use a zip-file. Also note that you are not supposed to do ML or Bayesian estimation on HP-filtered data.

Thanks for your reply, Johannes. The data file is attached.

Are you saying that the data file should contain unfiltered data? I was under the impression that all data files must be HP filtered prior to using them in estimation. Sounds like I am wrong.

EDIT: I have read through your document. This happens to be the first time I am using a model that I have not log-linearized by hand and used the model(linear) command, which is probably why I am running into those estimation problems. Your document states that the structure of the data and the structure of the model must be consistent. I would like to then use the loglinear command in the estimation function as in the fs2000 example that is included with dynare. I must admit, however, that I am not 100 percent certain of the transformation that was performed to the data file that is included with the fs2000 .mod file. From looking at the data, it definitely does not look like a log difference from HP filtered data. Again, I would like to use empirical real GDP to estimate a non-linear version of the basic RBC model, but I am unsure of what type of treatment to perform on the data file before launching the estimation.

Thanks again.
dataY.m (503 Bytes)

  1. The HP-filter is a two-sided filter and you should not use it for estimation other than direct inference.
  2. In any case, you are missing a proper observation equation. If you want to use HP-filtered data in any case, you must define something like

for your model variable to correspond to your data (of course you also need to rename your data in the datafile)
3. The data for the fs2000.mod is generated by simulating the model. Therefore, it corresponds perfectly to the model variables. In actual data, you would be using demeaned first differences. Note that when using first differences, you do not HP-filter the data in advance.
4. The standard way would be to use first differences. I added an example RBC model for Bayesian estimation doing exactly that. (7.9 KB)

I have a question regarding Table 2 when I run the RBC model in first differences (using Dynare 5.0). It says the p-value of convergence test is <0.05 for parameter rhog.

This means estimate in one part of the sample is significantly different from the other part of the sample, right?

So is this a problem? My interpretation would be that it is not a problem, because the standard error in the posterior is small, but this is just a guess.

Typically, if the MCMC has not converged to the ergodic distribution for one parameter yet, it has not yet converged in total. So results from estimation are meaningless, because the MCMC is still stuck in the transitory phase (subject to all the caveats with hypothesis testing).